{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f3bcfd94-2c57-4911-9ad2-65bac50937d9",
   "metadata": {},
   "source": [
    "Chapter 04\n",
    "\n",
    "# 逻辑函数分类，一元\n",
    "Book_7《机器学习》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cd7ae0be-dbda-4f20-9d59-4a516f705004",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ca47504-f1da-4dbc-9870-1100be71ea88",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_, y = load_iris(return_X_y=True)\n",
    "X = X_[:,0]\n",
    "X = X[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "699c30ee-2237-46cc-8cc0-90f5a9ffb680",
   "metadata": {},
   "outputs": [],
   "source": [
    "#%% KDE distributions of three classes \n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "iris = sns.load_dataset(\"iris\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9a8dd47a-e1bc-4edd-96d2-e3c0815fb73d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x132ea6981f0>,\n",
       "  <matplotlib.axis.XTick at 0x132ea6981c0>,\n",
       "  <matplotlib.axis.XTick at 0x132ea6d1ff0>,\n",
       "  <matplotlib.axis.XTick at 0x132ea6d23b0>,\n",
       "  <matplotlib.axis.XTick at 0x132ea6d2b00>],\n",
       " [Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, '')])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "sns.kdeplot(data=iris[['sepal_length','species']], x='sepal_length',\n",
    "            hue = 'species',\n",
    "            palette = \"viridis\",alpha=.3, linewidth=1,\n",
    "            fill=False)\n",
    "plt.xlabel('Sepal length, $x_1$')\n",
    "plt.xticks([4,5,6,7,8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ec5f45ac-017b-43b8-be74-3d773b143dad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "plt.scatter(X.ravel(), y, s = 8, alpha = 0.5, label = 'Original')\n",
    "plt.ylabel('Real y')\n",
    "plt.xlabel('Sepal length, $x_1$')\n",
    "plt.yticks([0,1,2])\n",
    "plt.xticks([4,5,6,7,8])\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "da8f1f11-7d85-419c-9c86-e24ba21e9676",
   "metadata": {},
   "outputs": [],
   "source": [
    "#%% logistic regression\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X, y)\n",
    "\n",
    "X_test = np.linspace(X.min()*0.9,X.max()*1.1,num = 100)\n",
    "X_test = X_test[:, np.newaxis]\n",
    "\n",
    "y_hat = clf.predict(X_test)\n",
    "y_prob = clf.predict_proba(X_test)\n",
    "\n",
    "b1 = clf.coef_\n",
    "b0 = clf.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5ff6ab58-5373-4fe3-ba30-1505b189681e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% probabilities\n",
    "\n",
    "x = np.linspace(X.min()*0.9,X.max()*1.1,num = 100);\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.plot(X_test, y_prob[:,0], color='r', \n",
    "         linewidth=1, label = 'Class 0')\n",
    "plt.fill_between(x, y_prob[:,0], color='r', alpha = 0.5)\n",
    "\n",
    "plt.plot(X_test, y_prob[:,1], color='b', \n",
    "         linewidth=1, label = 'Class 1')\n",
    "plt.fill_between(x, y_prob[:,1], color='b', alpha = 0.5)\n",
    "\n",
    "plt.plot(X_test, y_prob[:,2], color='g', \n",
    "         linewidth=1, label = 'Class 2')\n",
    "plt.fill_between(x, y_prob[:,2], color='g', alpha = 0.5)\n",
    "\n",
    "plt.ylabel('Probability')\n",
    "plt.xlabel('Sepal length, $x_1$')\n",
    "plt.xticks([4,5,6,7,8])\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4a628e52-0b12-4665-b0e5-462172219e28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% Predicted y\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "plt.scatter(X.ravel(), clf.predict(X), s = 8, \n",
    "            alpha = 0.5, label = 'Predicted')\n",
    "\n",
    "plt.ylabel('Predicted y')\n",
    "plt.xlabel('Sepal length, $x_1$')\n",
    "plt.yticks([0,1,2])\n",
    "plt.xticks([4,5,6,7,8])\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
